- Email: [email protected]
Study on the methods of image enhancement for liver CT images
Optik 121 (2010) 1752–1755
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Study on the methods of image enhancement for liver CT images Li Yang a, Yanmei Liang a,, Hailun Fan b a b
Key Laboratory of Opto-electronic Information Science and Technology, Ministry of Education, Institute of Modern Optics, Nankai University, Tianjin 300071, PR China Department of Radiology, Tianjin Medical University General Hospital, Tianjin 300052, PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 16 December 2008 Accepted 21 April 2009
Image enhancement methods for liver CT images are studied in this paper. The liver region is first segmented from the whole CT image by simply using the characteristics of the gray distribution of the liver. The segmented liver CT image is processed by direct gray stretching, logarithmic transformation and linear stretching with histogram fitting. In addition, the method of selective histogram equalization is proposed to enhance the segmented liver CT image. It is proven from the experimental results that by this two-step method, the visual effect of the segmented image can be effectively improved and the focus is obviously highlighted. Crown Copyright & 2009 Published by Elsevier GmbH. All rights reserved.
Keywords: Liver CT image Image segmentation Image enhancement
1. Introduction As a medical imaging technique, computed tomography (CT) is quite useful for doctors to analyze the pathological changes of the biological organs. In order to reduce deaths, the diseases must be detected accurately in the early stage. However, the inherent lowdensity resolution makes CT images for the biological parenchyma, such as the liver, often have low contrast, which sometimes makes doctors judge inaccurately. Some contrast agents can be injected to enhance the CT image, but they are harmful to the patient, and lethal to some patients because of anaphylaxis. Medical image processing, as an assistant means, can play an important role in early diagnosis. Some processing methods have been proposed to segment the related organ from the whole medical images [1–3] or analyze and classify the texture [4–6]. However, because of the complicated textures and low gray differences in liver CT images, for some early local pathological changes, such as liver cancers, hepatic abscess, etc., the changes of gray levels are too small to be noticed, it would be a great challenge even for some experienced doctors to make a right diagnosis. Currently, there are some image enhancement methods. Histogram equalization (HE) is a common way to improve contrast, which generates an image whose pixels of gray levels are as equal as possible. But for the original CT image, because of the large low gray background, HE often makes the whole image too bright to see [7,8]. In recent years, contrast limited adaptive histogram equalization (CLAHE) has been used in medical images
Corresponding author.
E-mail address: [email protected] (Y. Liang).
processing [7]. However, it is easy to introduce artificial boundaries at the region where gray levels have great differences. In this paper, a two-step method is proposed to effectively enhance the liver region. The liver region is firstly segmented from the CT image with a simple segmentation method, certain algorithm is then used to enhance the contrast of the segmented liver image. Several enhancement algorithms are explored and compared. From the experimental results, the liver focus can be obviously distinguished from the normal liver tissue, which will help doctors to diagnose the forepart focus correctly.
2. The methods of image enhancement Generally, the gray levels of a digital CT image cover from 0 to 255, but the gray levels of the liver region cover a small range, so it is difficult to do enhancement on the original digital CT image effectively. In this paper, the liver region is firstly segmented from the original image to form a new image which only includes the liver region and a black background. Then the enhancement algorithms are done on the segmented image. 2.1. Segmentation of the liver CT image Because the liver is the biggest organ in the liver CT image, a simple but effective way to segment the liver is used to reduce the processing time. The segmentation procedures are as follows: (1) Find out the gray level that appears most in the original image except the gray level 0 and 255. (2) Take the gray level as a center, reserve the gray levels within a certain radius around the center level, and set other pixels’ gray level as 0. Then, some discrete blocks in the CT image are
0030-4026/$ - see front matter Crown Copyright & 2009 Published by Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2009.04.006
L. Yang et al. / Optik 121 (2010) 1752–1755
obtained. The above two steps can be called gray levels filtering. (3) Reserve the block whose area is the biggest and set the others as 0. (4) Set the reserved block’s gray levels as 255. Execute morphologic close operation and fill the holes in the block using gray level 255. The liver denoted with the gray level 255 is segmented. (5) Fill in the regions which have gray level 255 using the gray levels in original CT image in the same region. The nearly entire liver region denoted with its original gray levels is obtained from the CT image.
2.2. Enhancement algorithms Several enhancement algorithms are adopted in this paper, which are described as follows: (1) Direct stretching with the linear relationship: The purpose of the image enhancement is to improve the image contrast, which transforms the gray range in the original image into a relatively larger range. If the transform function I0 ¼ T(I) is a linear single-valued function, this treatment is called gray linear transform, or linear stretching, which can be performed with the following formula by direct stretching: I0 ¼
0 0 Imax Imin 0 ðI Imin Þ þ Imin ; Imax Imin
ð1Þ
where I and I0 are the gray levels before and after transformation, respectively. I0 max and I0 min are the highest and lowest gray level after transformation, Imax and Imin are the maximum and minimum gray level in the liver region before the transformation, respectively. (2) Linear stretching according to the fitting curve: The histogram of the segmented liver CT region is more like a normal distrubution [9], so Gaussian function can be used to fit the histogram in order to determine the range which should be transformed. The Gaussian function is described as 2
PðxÞ ¼ ceðxaÞ
=b2
:
1753
move to the low gray levels. The formula of this transformation is described as follows: I0 ¼ C log10 ð1 þ jI Imin jÞ;
ð3Þ
where I and I0 are the gray levels before and after transformation, respectively. C is a constant which determines the range of the gray levels after transformation; Imin is the minimum gray level of the liver region before transformation. (4) Selective histogram equalization: The conventional histogram equalization (HE) is to enhance the whole image, so if there are large low gray level regions in the image, the enhanced result will be too bright and cannot improve the visual effect. The method of selective histogram equalization is to choose the interested regions to do histogram equalization and leave others alone. Based on the segmented liver image, the histogram of the liver region can be obtained easily. Then executing histogram equalization on this histogram enhances the liver region.
3. Experimental results and discussions A 512 512 liver cancer CT image is used in this paper. The original image is shown in Fig. 1(a). The image after gray levels filtering is shown in Fig. 1(b), where the center gray level is 161, and the reserved radius of gray level is 30. The image after the close operation and the segmented liver image are respectively shown in Figs. 1(c) and 1(d). From Fig. 1(d), the gray difference between the focus marked by a real line rectangular box and the healthy part is inconspicuous, so the cancer region cannot be clearly distinguished from the healthy part without careful observation. The curve of the gray levels from an arbitrarily selected row marked by a horizontal line in Fig. 1(d) is shown in Fig. 2. It can be
ð2Þ
The parameter a represents the position of the peak center, b controls the width of the curve, and c is the height of the curve’s peak. In this paper, the algorithm of the least squares fitting is used to fit the histogram of the segmented liver CT region [10] and obtain the values of a, b, and c. Then Eq. (1) is used to stretch the gray range. The gray levels of the image lower than the minimum of the transformed range will be set as 0, and the levels higher than the maximum of the transformed range will be set as 255. The transformed range [Imin, Imax] is depended on a and b. According to the definition of the normal school, the gray range [ab, a+b] in the gray level can cover about 84% pixels of the liver, the range [a2b, a+2b] can cover about 99% pixels of the liver, and [a3b, a+3b] will cover about all of the liver. (3) Nonlinear stretching with the logarithmic transformation: If the transform function I0 ¼ T(I) is a nonlinear single-value function, the transformation is called gray nonlinear transformation. The logarithm transformation is often used to stretch low gray level, and compress high gray level. Therefore, the details of low gray region can be distinguished more clearly. Here the minimum gray level in the liver region will be subtracted from the image before transformed and thus all gray levels will
Fig. 1. A liver CT image. (a) An original liver CT image; (b) the result after gray level filtering; (c) the result after the close operation and filling the holes; (d) the final segmented liver image (the region in and around the real rectangular box represents the focus).
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L. Yang et al. / Optik 121 (2010) 1752–1755
Fig. 2. The curve of the gray levels from an arbitrarily selected row shown by a white line in Fig. 1(d). The focus is signed with a thin curve and the healthy part is signed with the thick curves.
Fig. 3. The distribution of gray levels in the liver region with dots and its fitting Gaussian curve with a blue line. The Y-axis presents the normalized probability density of the gray levels.
seen that the gray levels of the focus are slightly less than those of the healthy part around it. The distribution of gray levels of the liver region of Fig. 1(d) is given in Fig. 3 with dots, and the fitting result with Gaussian function is expressed with a blue curve. Fig. 1(d) is enhanced by the methods described in Section 2.2. The results are shown in Figs. 4(a–f). Where C is chosen 3.075 in logarithmic transformation; a is 162.7; and b is 16.01 in Gaussian fitting from Fig. 3. The highest and lowest gray level after transformation, I0 max and I0 min, is 255 and 0 for all these methods, respectively. The quality of the liver image has been improved from Fig. 4. The contrast between the healthy part and the focus is used to evaluate these methods. Two regions are selected in Fig. 1(d), of which a dashed rectangular box represents the healthy part and the real rectangular box represents the focus. The average gray levels of the two regions, Ihealthy and Ifocus, are calculated. The contrast between them is given by the formula I healthy Ifocus Contrast ¼ ð4Þ : Ihealthy þ Ifocus The same regions as Fig. 1(d) in Figs. 4(a)–(f) are used to calculate their contrasts. The results are shown in Table 1.
Fig. 4. The liver CT enhanced images. (a) Direct stretching with the linear relationship, (b) logarithmic transformation (C ¼ 3.075), (c) linear stretching with Gaussian fitting in the range of [ab, a+b], (d) linear stretching with Gaussian fitting in the range of [a2b, a+2b], (e) linear stretching with Gaussian fitting in the range of [a3b, a+3b], (f) the selective histogram equalization.
Table 1 Contrast of the original image and the enhanced images. Methods Fig. 1(d) Fig. 4(a) Fig. 4(b) Fig. 4(c) Fig. 4(d) Fig. 4(e) Fig. 4(f) Contrast
0.04
0.11
0.10
0.46
0.26
0.16
0.33
From Table 1, compared with the original image, the processed images have been enhanced in different degrees. The linear and logarithm stretching are easy to execute. The initial stretching range in linear and logarithm stretching is just selected by the minimum and the maximum of the gray levels of the liver. The minimum and the maximum are easy to be influenced by the noise. So the range may be too large or too small because of the noise. A wide initial stretching range may result in an inconspicuous improvement, while a narrow stretching range may result in over enhancement and lose the microstructure of the focus texture. The linear stretching with Gaussian fitting in the range of [ab, a+b] has the largest contrast enhancement, but the stretching
L. Yang et al. / Optik 121 (2010) 1752–1755
1755
the enhanced result shown in Fig. 5(b), the peripheral walls of the abscess lesions enclosed by the rectangular box are clearer than the unprocessed image.
4. Conclusion
Fig. 5. A hepatic abscess CT image. (a) The original CT image, (b) the result of linear stretching with Gaussian fitting in the range of [a3b, a+3b] (a ¼ 156.60, b ¼ 15.76).
range is appreciably small, and introduces a little over enhancement. The linear stretching with Gaussian fitting in the range of [a2b, a+2b] and [a3b, a+3b] have smaller contrast enhancement than that of the range of [ab, a+b], but they have better performances, which the microstructure of the focus texture can be clearly distinguished. The range which is determined by Gaussian fitting is based on the whole gray levels of the liver region, so it can reduce the influence of the noise in a certain extent. The selective histogram equalization has the second largest contrast enhancement, and this algorithm is also based on the whole gray levels of the liver region, so it can reduce the influence of the noise. In practice, for selecting the stretching range, there is a tradeoff between reducing the noise in the image and avoiding over enhancement. In addition, the gray levels of the CT image are proportional to the densities of the organ, so all enhanced methods should only change the distances between gray levels, but cannot change their orders in the histogram. Another 512 512 hepatic abscess CT image is shown in Fig. 5(a). It is segmented, by using the procedure of Section 2.1, of which the center gray level is 158, and the reserved radius of gray level is 30. The segmented liver CT image is enhanced by linear stretching with Gaussian fitting in the range of [a3b, a+3b]. From
The methods of image enhancement based on the segmented liver CT images are performed, which can effectively stretch the gray of liver region and highlight the lesions. In all the transformations, the selective histogram equalization, linear, and logarithm stretching are simple and easy to execute, but the range of transformation can be obtained adaptively by fitting the histogram with the Gaussian curve, which can achieve a better effect according to different CT images. Distinguishing the focus automatically with some algorithms based on the enhanced images will be our future work.
Acknowledgements This research is supported the National Natural Science Foundation of China (Grant No. 60677012) and the Tianjin Foundation of Natural Science (Grant No. 09JCZDJC18300). References [1] F. Liu, B. Zhao, P.K. Kijewski, L. Wang, L.H. Schwartz, Med. Phys. 32 (2005) 3699–3706. [2] A. Yezzi, S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, IEEE Trans. Med. Imaging 16 (1997) 199–209. [3] S. Wang, D. Fu, M. Xu, D. Hu, Artif. Intell. Med. 39 (2007) 65–77. [4] A.H. Mir, M. Hanmandlu, S.N. Tandon, Eng. Med. Biol. Mag. IEEE 14 (1995) 781–786. [5] S.M. Yamany, K.J. Khiani, A.A. Farag, Pattern Recognition Lett. 18 (1997) 1205– 1210. [6] S. Mougiakakou, I. Valavanis, A. Nikita, K. Nikita, Artif. Intell. Med. 41 (2007) 25–37. [7] Y. Jin, L. Fayad, A. Laine, SPIE Proc. 4478 (2001) 206–213. [8] J.A. Stark, IEEE Trans. Image Process. 9 (2000) 889–896. [9] S.J. Lim, Y.Y. Jeong, Y.S. Ho, Advances in Multimedia Information ProcessingPCM 2005, vol. 3767, Springer, Berlin, Heidelberg, 2005. [10] Y. Liu, Y. Liang, Z. Tong, X. Zhu, G. Mu, Opt. Commun. 279 (2007) 23–26.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Study on the methods of image enhancement for liver CT images Li Yang a, Yanmei Liang a,, Hailun Fan b a b
Key Laboratory of Opto-electronic Information Science and Technology, Ministry of Education, Institute of Modern Optics, Nankai University, Tianjin 300071, PR China Department of Radiology, Tianjin Medical University General Hospital, Tianjin 300052, PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 16 December 2008 Accepted 21 April 2009
Image enhancement methods for liver CT images are studied in this paper. The liver region is first segmented from the whole CT image by simply using the characteristics of the gray distribution of the liver. The segmented liver CT image is processed by direct gray stretching, logarithmic transformation and linear stretching with histogram fitting. In addition, the method of selective histogram equalization is proposed to enhance the segmented liver CT image. It is proven from the experimental results that by this two-step method, the visual effect of the segmented image can be effectively improved and the focus is obviously highlighted. Crown Copyright & 2009 Published by Elsevier GmbH. All rights reserved.
Keywords: Liver CT image Image segmentation Image enhancement
1. Introduction As a medical imaging technique, computed tomography (CT) is quite useful for doctors to analyze the pathological changes of the biological organs. In order to reduce deaths, the diseases must be detected accurately in the early stage. However, the inherent lowdensity resolution makes CT images for the biological parenchyma, such as the liver, often have low contrast, which sometimes makes doctors judge inaccurately. Some contrast agents can be injected to enhance the CT image, but they are harmful to the patient, and lethal to some patients because of anaphylaxis. Medical image processing, as an assistant means, can play an important role in early diagnosis. Some processing methods have been proposed to segment the related organ from the whole medical images [1–3] or analyze and classify the texture [4–6]. However, because of the complicated textures and low gray differences in liver CT images, for some early local pathological changes, such as liver cancers, hepatic abscess, etc., the changes of gray levels are too small to be noticed, it would be a great challenge even for some experienced doctors to make a right diagnosis. Currently, there are some image enhancement methods. Histogram equalization (HE) is a common way to improve contrast, which generates an image whose pixels of gray levels are as equal as possible. But for the original CT image, because of the large low gray background, HE often makes the whole image too bright to see [7,8]. In recent years, contrast limited adaptive histogram equalization (CLAHE) has been used in medical images
Corresponding author.
E-mail address: [email protected] (Y. Liang).
processing [7]. However, it is easy to introduce artificial boundaries at the region where gray levels have great differences. In this paper, a two-step method is proposed to effectively enhance the liver region. The liver region is firstly segmented from the CT image with a simple segmentation method, certain algorithm is then used to enhance the contrast of the segmented liver image. Several enhancement algorithms are explored and compared. From the experimental results, the liver focus can be obviously distinguished from the normal liver tissue, which will help doctors to diagnose the forepart focus correctly.
2. The methods of image enhancement Generally, the gray levels of a digital CT image cover from 0 to 255, but the gray levels of the liver region cover a small range, so it is difficult to do enhancement on the original digital CT image effectively. In this paper, the liver region is firstly segmented from the original image to form a new image which only includes the liver region and a black background. Then the enhancement algorithms are done on the segmented image. 2.1. Segmentation of the liver CT image Because the liver is the biggest organ in the liver CT image, a simple but effective way to segment the liver is used to reduce the processing time. The segmentation procedures are as follows: (1) Find out the gray level that appears most in the original image except the gray level 0 and 255. (2) Take the gray level as a center, reserve the gray levels within a certain radius around the center level, and set other pixels’ gray level as 0. Then, some discrete blocks in the CT image are
0030-4026/$ - see front matter Crown Copyright & 2009 Published by Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2009.04.006
L. Yang et al. / Optik 121 (2010) 1752–1755
obtained. The above two steps can be called gray levels filtering. (3) Reserve the block whose area is the biggest and set the others as 0. (4) Set the reserved block’s gray levels as 255. Execute morphologic close operation and fill the holes in the block using gray level 255. The liver denoted with the gray level 255 is segmented. (5) Fill in the regions which have gray level 255 using the gray levels in original CT image in the same region. The nearly entire liver region denoted with its original gray levels is obtained from the CT image.
2.2. Enhancement algorithms Several enhancement algorithms are adopted in this paper, which are described as follows: (1) Direct stretching with the linear relationship: The purpose of the image enhancement is to improve the image contrast, which transforms the gray range in the original image into a relatively larger range. If the transform function I0 ¼ T(I) is a linear single-valued function, this treatment is called gray linear transform, or linear stretching, which can be performed with the following formula by direct stretching: I0 ¼
0 0 Imax Imin 0 ðI Imin Þ þ Imin ; Imax Imin
ð1Þ
where I and I0 are the gray levels before and after transformation, respectively. I0 max and I0 min are the highest and lowest gray level after transformation, Imax and Imin are the maximum and minimum gray level in the liver region before the transformation, respectively. (2) Linear stretching according to the fitting curve: The histogram of the segmented liver CT region is more like a normal distrubution [9], so Gaussian function can be used to fit the histogram in order to determine the range which should be transformed. The Gaussian function is described as 2
PðxÞ ¼ ceðxaÞ
=b2
:
1753
move to the low gray levels. The formula of this transformation is described as follows: I0 ¼ C log10 ð1 þ jI Imin jÞ;
ð3Þ
where I and I0 are the gray levels before and after transformation, respectively. C is a constant which determines the range of the gray levels after transformation; Imin is the minimum gray level of the liver region before transformation. (4) Selective histogram equalization: The conventional histogram equalization (HE) is to enhance the whole image, so if there are large low gray level regions in the image, the enhanced result will be too bright and cannot improve the visual effect. The method of selective histogram equalization is to choose the interested regions to do histogram equalization and leave others alone. Based on the segmented liver image, the histogram of the liver region can be obtained easily. Then executing histogram equalization on this histogram enhances the liver region.
3. Experimental results and discussions A 512 512 liver cancer CT image is used in this paper. The original image is shown in Fig. 1(a). The image after gray levels filtering is shown in Fig. 1(b), where the center gray level is 161, and the reserved radius of gray level is 30. The image after the close operation and the segmented liver image are respectively shown in Figs. 1(c) and 1(d). From Fig. 1(d), the gray difference between the focus marked by a real line rectangular box and the healthy part is inconspicuous, so the cancer region cannot be clearly distinguished from the healthy part without careful observation. The curve of the gray levels from an arbitrarily selected row marked by a horizontal line in Fig. 1(d) is shown in Fig. 2. It can be
ð2Þ
The parameter a represents the position of the peak center, b controls the width of the curve, and c is the height of the curve’s peak. In this paper, the algorithm of the least squares fitting is used to fit the histogram of the segmented liver CT region [10] and obtain the values of a, b, and c. Then Eq. (1) is used to stretch the gray range. The gray levels of the image lower than the minimum of the transformed range will be set as 0, and the levels higher than the maximum of the transformed range will be set as 255. The transformed range [Imin, Imax] is depended on a and b. According to the definition of the normal school, the gray range [ab, a+b] in the gray level can cover about 84% pixels of the liver, the range [a2b, a+2b] can cover about 99% pixels of the liver, and [a3b, a+3b] will cover about all of the liver. (3) Nonlinear stretching with the logarithmic transformation: If the transform function I0 ¼ T(I) is a nonlinear single-value function, the transformation is called gray nonlinear transformation. The logarithm transformation is often used to stretch low gray level, and compress high gray level. Therefore, the details of low gray region can be distinguished more clearly. Here the minimum gray level in the liver region will be subtracted from the image before transformed and thus all gray levels will
Fig. 1. A liver CT image. (a) An original liver CT image; (b) the result after gray level filtering; (c) the result after the close operation and filling the holes; (d) the final segmented liver image (the region in and around the real rectangular box represents the focus).
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L. Yang et al. / Optik 121 (2010) 1752–1755
Fig. 2. The curve of the gray levels from an arbitrarily selected row shown by a white line in Fig. 1(d). The focus is signed with a thin curve and the healthy part is signed with the thick curves.
Fig. 3. The distribution of gray levels in the liver region with dots and its fitting Gaussian curve with a blue line. The Y-axis presents the normalized probability density of the gray levels.
seen that the gray levels of the focus are slightly less than those of the healthy part around it. The distribution of gray levels of the liver region of Fig. 1(d) is given in Fig. 3 with dots, and the fitting result with Gaussian function is expressed with a blue curve. Fig. 1(d) is enhanced by the methods described in Section 2.2. The results are shown in Figs. 4(a–f). Where C is chosen 3.075 in logarithmic transformation; a is 162.7; and b is 16.01 in Gaussian fitting from Fig. 3. The highest and lowest gray level after transformation, I0 max and I0 min, is 255 and 0 for all these methods, respectively. The quality of the liver image has been improved from Fig. 4. The contrast between the healthy part and the focus is used to evaluate these methods. Two regions are selected in Fig. 1(d), of which a dashed rectangular box represents the healthy part and the real rectangular box represents the focus. The average gray levels of the two regions, Ihealthy and Ifocus, are calculated. The contrast between them is given by the formula I healthy Ifocus Contrast ¼ ð4Þ : Ihealthy þ Ifocus The same regions as Fig. 1(d) in Figs. 4(a)–(f) are used to calculate their contrasts. The results are shown in Table 1.
Fig. 4. The liver CT enhanced images. (a) Direct stretching with the linear relationship, (b) logarithmic transformation (C ¼ 3.075), (c) linear stretching with Gaussian fitting in the range of [ab, a+b], (d) linear stretching with Gaussian fitting in the range of [a2b, a+2b], (e) linear stretching with Gaussian fitting in the range of [a3b, a+3b], (f) the selective histogram equalization.
Table 1 Contrast of the original image and the enhanced images. Methods Fig. 1(d) Fig. 4(a) Fig. 4(b) Fig. 4(c) Fig. 4(d) Fig. 4(e) Fig. 4(f) Contrast
0.04
0.11
0.10
0.46
0.26
0.16
0.33
From Table 1, compared with the original image, the processed images have been enhanced in different degrees. The linear and logarithm stretching are easy to execute. The initial stretching range in linear and logarithm stretching is just selected by the minimum and the maximum of the gray levels of the liver. The minimum and the maximum are easy to be influenced by the noise. So the range may be too large or too small because of the noise. A wide initial stretching range may result in an inconspicuous improvement, while a narrow stretching range may result in over enhancement and lose the microstructure of the focus texture. The linear stretching with Gaussian fitting in the range of [ab, a+b] has the largest contrast enhancement, but the stretching
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the enhanced result shown in Fig. 5(b), the peripheral walls of the abscess lesions enclosed by the rectangular box are clearer than the unprocessed image.
4. Conclusion
Fig. 5. A hepatic abscess CT image. (a) The original CT image, (b) the result of linear stretching with Gaussian fitting in the range of [a3b, a+3b] (a ¼ 156.60, b ¼ 15.76).
range is appreciably small, and introduces a little over enhancement. The linear stretching with Gaussian fitting in the range of [a2b, a+2b] and [a3b, a+3b] have smaller contrast enhancement than that of the range of [ab, a+b], but they have better performances, which the microstructure of the focus texture can be clearly distinguished. The range which is determined by Gaussian fitting is based on the whole gray levels of the liver region, so it can reduce the influence of the noise in a certain extent. The selective histogram equalization has the second largest contrast enhancement, and this algorithm is also based on the whole gray levels of the liver region, so it can reduce the influence of the noise. In practice, for selecting the stretching range, there is a tradeoff between reducing the noise in the image and avoiding over enhancement. In addition, the gray levels of the CT image are proportional to the densities of the organ, so all enhanced methods should only change the distances between gray levels, but cannot change their orders in the histogram. Another 512 512 hepatic abscess CT image is shown in Fig. 5(a). It is segmented, by using the procedure of Section 2.1, of which the center gray level is 158, and the reserved radius of gray level is 30. The segmented liver CT image is enhanced by linear stretching with Gaussian fitting in the range of [a3b, a+3b]. From
The methods of image enhancement based on the segmented liver CT images are performed, which can effectively stretch the gray of liver region and highlight the lesions. In all the transformations, the selective histogram equalization, linear, and logarithm stretching are simple and easy to execute, but the range of transformation can be obtained adaptively by fitting the histogram with the Gaussian curve, which can achieve a better effect according to different CT images. Distinguishing the focus automatically with some algorithms based on the enhanced images will be our future work.
Acknowledgements This research is supported the National Natural Science Foundation of China (Grant No. 60677012) and the Tianjin Foundation of Natural Science (Grant No. 09JCZDJC18300). References [1] F. Liu, B. Zhao, P.K. Kijewski, L. Wang, L.H. Schwartz, Med. Phys. 32 (2005) 3699–3706. [2] A. Yezzi, S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, IEEE Trans. Med. Imaging 16 (1997) 199–209. [3] S. Wang, D. Fu, M. Xu, D. Hu, Artif. Intell. Med. 39 (2007) 65–77. [4] A.H. Mir, M. Hanmandlu, S.N. Tandon, Eng. Med. Biol. Mag. IEEE 14 (1995) 781–786. [5] S.M. Yamany, K.J. Khiani, A.A. Farag, Pattern Recognition Lett. 18 (1997) 1205– 1210. [6] S. Mougiakakou, I. Valavanis, A. Nikita, K. Nikita, Artif. Intell. Med. 41 (2007) 25–37. [7] Y. Jin, L. Fayad, A. Laine, SPIE Proc. 4478 (2001) 206–213. [8] J.A. Stark, IEEE Trans. Image Process. 9 (2000) 889–896. [9] S.J. Lim, Y.Y. Jeong, Y.S. Ho, Advances in Multimedia Information ProcessingPCM 2005, vol. 3767, Springer, Berlin, Heidelberg, 2005. [10] Y. Liu, Y. Liang, Z. Tong, X. Zhu, G. Mu, Opt. Commun. 279 (2007) 23–26.